In the previous Mishnah, thirty-six transgressions were listed for which the punishment is kares. Now the Mishnah arrives at the point it was driving toward: what is the law for one who transgresses one of them, and under what circumstances.
The Three States of Liability:
"Al elu chayavin al zedonan kares" - One who transgresses intentionally, his punishment is kares, that Divine severance explained in the introduction.
"Ve'al shigegatam chatas" - One who transgresses one of these matters unintentionally, who committed a sinful act without intent, is obligated to bring a chatas offering.
"Ve'al lo hoda shelahen" - One who does not know with certainty whether he transgressed. For example, he knows that he cohabited with a woman, but he does not know whether she was his mother or not.
The chatas mentioned here is a fixed chatas, meaning a female goat or a female sheep in its first year, and this is the regular situation. In a case of doubt, one cannot bring a chatas, since there is no such thing as bringing a chatas out of doubt, as we will see later. Instead, the person brings an asham taluy - the suspensive asham offering: not a female goat or sheep, but a ram, a male sheep aged a year, a month, and a day. This offering suspends the consequences of the severe transgression, and if it later becomes clear who or what the situation was, and it becomes clear that he was indeed liable - he will then bring an additional offering as a chatas, if he is obligated to do so.
The Exceptions:
This rule is stated regarding the list of thirty-six, but there are a few exceptions: "Chutz min hametamei mikdash vekodashav" - A person who is tamei and enters the Temple area, or who is tamei and eats consecrated items, whether menachos, zevachim, or the like. Entering and eating are forbidden to him, and if he transgressed and did so, his obligation is not a fixed chatas but an oleh veyored offering, the chatas offering that fluctuates according to what he can afford:
If he can afford to bring a female goat or female sheep - he is obligated in those.
And if he cannot afford it - he brings two birds: two turtledoves (wild turtledoves) or two young pigeons (pigeon chicks).
And if he is so poor that he cannot even afford the two birds - he brings a minchas chotei, the simple fine flour minchah of a sinner.
Since the offering of these two fluctuates and is not fixed, it emerges that they do not have a fixed chatas but an oleh veyored offering, and consequently they do not have an asham taluy either - because the asham taluy comes specifically in a place where there is doubt regarding the obligation of a fixed chatas. These are the words of Rabbi Meir, and this is his approach.
The Dispute Between Rabbi Meir and the Sages Regarding a Megadef:
The Sages agree with this, but they add one more thing to the list of exceptions: "Af hamegadef" - He is one who mentions the Name of God in order to bless the Name, as was explained previously, who speaks against Heaven.
And their source is from the verse: "Torah achas tihyeh lachem la'oseh bishgagah" - We learn that the obligation applies to the one who acts, to one who does a deed unintentionally, without intent to transgress the prohibition. This rule, which is stated regarding idol worship, is applied as well to the other transgressions that carry a liability of kares. But here, since there is no action involved - "Yatza megadef she'eino oseh maaseh" - The megadef does nothing but speak alone, and according to the Sages, speech is not considered an action. Therefore, the megadef too is exempt from bringing a chatas if he acted unintentionally.
Rabbi Meir disagrees and follows the approach known as the approach of Rabbi Akiva: The rule of a negative prohibition that involves no action does not exempt, and even one who transgresses through speech alone is included in the obligation. Therefore, according to Rabbi Meir following the approach of Rabbi Akiva, the megadef is obligated to bring a fixed chatas. And the halachah follows the Sages.
The Actual Calculation:
In light of this, the words of the Rambam work out as follows: Even though the Mishnah listed thirty-six, as stated, there are ultimately forty-eight. The Rambam writes explicitly that forty-three transgressions require a fixed Chatas. Meaning: there are forty-eight transgressions punishable by kares, but only forty-three of them require a Chatas when committed inadvertently.
What, then, are the five cases that make up the difference?
A tamei person who enters the Beis HaMikdash.
A tamei person who ate kodashim - these two were listed explicitly in our Mishnah, and they do not require a fixed Chatas, but rather a sliding-scale offering (korban oleh veyored).
A blasphemer - which carries a liability for kares, but does not require a fixed Chatas because it does not involve a physical action.
Failure to perform circumcision (bris milah).
Refraining from participating in the Pesach sacrifice - these two were listed in the previous Mishnah, and even though they carry a liability for kares, since they are positive commandments, they do not require a Chatas.
In summary: These five cases, when deducted from the total of forty-eight, bring us to forty-three - the number of transgressions that carry a liability for a fixed Chatas when a person commits them inadvertently.